Considering molar mass of
$ Ar->40" g/mol"$
$ Ne->20" g/mol"$
$ "Molar mass of unknown gas"->m" g/mol"$
The total number of moles Ar , Ne and unknown gas in the gas mixture each having mass of 7g is
$=(7/40+7/20+7/m)mol$
Total Volume of these three gases at STP is
$(7/40+7/20+7/m)molxx22.4L/"mol"=16.60L$
$=>(7/40+7/20)22.4L+7/mxx22.4L=16.60L$
$=>21/40xx22.4+7/mxx22.4=16.60$
$=>11.76+7/mxx22.4=16.60$
$=>7/mxx22.4=(16.60-11.76)=4.24$
$=>m=(7xx22.4)/4.24~~36.98"g/mol"$